On the Benefits of Two Dimensional Metric Learning

In this paper, we study two dimensional metric learning (2DML) for matrix data from both theoretical and algorithmic perspectives. We first investigate the generalization bounds of 2DML based on the notion of Rademacher complexity, which theoretically justifies the benefits of learning from matrices directly. Furthermore, we present a novel boosting-based algorithm that scales well with the feature dimension. Finally, we introduce an efficient rank-one correction algorithm, which is tailored to our boosting learning procedure to produce a low-rank solution to 2DML. As our algorithm works directly on the data in matrix representation, it scales well with the feature dimension, keeps the structure and dependence in the data, and has a more compact structure and much fewer parameters to optimize. Extensive evaluations on several benchmark data sets also empirically verify the effectiveness and efficiency of our algorithm.